Quantum computing and the stable set problemKrpan, Aljaž (Avtor) Povh, Janez (Avtor) Pucher, Dunja (Avtor) stable set problemquantum annealinggraph partitioningD-WaveGiven an undirected graph, the stable set problem asks to determine the cardinality of the largest subset of pairwise non-adjacent vertices. This value is called the stability number of the graph, and its computation is an NP-hard problem. In this paper, we solve the stable set problem using the D-Wave quantum annealer. By formulating the problem as a quadratic unconstrained binary optimization problem with the penalty method, we show its optimal value equals the graph's stability number for specific penalty values. However, D-Wave's quantum annealer is a heuristic, so the solutions may be far from the optimum and may not represent stable sets. To address these, we introduce a post-processing procedure that identifies samples that could lead to improved solutions. Additionally, we propose a partitioning method to handle larger instances that cannot be embedded on D-Wave's quantum processing unit. Finally, we investigate how different penalty parameter values affect the solutions' quality. Extensive computational results show that the post-processing procedure significantly improves the solution quality, while the partitioning method successfully extends our approach to medium-size instances.Taylor & Francis Group20252025-10-17 03:49:21Neznano23885sl© 2025 The Author(s)